If and

is necessarily a Prime? In other words, defining

does there exist a Composite such that ? It is known that Iff for each prime divisor of , and (Giuga 1950, Borwein

**References**

Bedocchi, E. ``The
Ring and the Euclidean Algorithm.'' *Manuscripta Math.* **53**, 199-216, 1985.

Borwein, D.; Borwein, J. M.; Borwein, P. B.; and Girgensohn, R. ``Giuga's Conjecture on Primality.''
*Amer. Math. Monthly* **103**, 40-50, 1996.

Giuga, G. ``Su una presumibile propertietà caratteristica dei numeri primi.''
*Ist. Lombardo Sci. Lett. Rend. A* **83**, 511-528, 1950.

Ribenboim, P. *The Book of Prime Number Records, 2nd ed.* New York: Springer-Verlag, pp. 20-21, 1989.

© 1996-9

1999-05-25